Marvel is on the verge of casting the actor to play their teenaged Spider-Man, with the six finalists testing during the shoot of Captain America: Civil War where the character will debut. While that will be where Spider-Man is first seen, it may not be where he's first mentioned. A rumor from Latino Review suggests Spider-Man could be referenced in Ant-Man, which opens in just a couple of months.
A number of rewrites have been done to the Ant-Man screenplay since Edgar Wright departed, and apparently part of that was to add references to Spider-Man. This way they can allude to his origin without having to revisit it again in the future. We may also see the villain Darren Cross (Corey Stoll) try to sell the Yellowjacket armor to other corporations, and one of them could be OsCorp. All of this is speculation and may not even happen, but it would make sense to name drop Spidey early if it can be done without going overboard.
For now, Marvel has revealed a new poster and a dozen images from Ant-Man featuring stars Paul Rudd, Michael Douglas, Evangeline Lilly, and Corey Stoll. Directed by Peyton Reed, the film opens on July 17th.
